Spatial mapping of b-value and fractal dimension prior to November 8, 2022 Doti Earthquake, Nepal

An earthquake of magnitude 5.6 mb (6.6 ML) hit western Nepal (Doti region) in the wee hours of wednesday morning local time (2:12 AM, 2022.11.08) killing at least six people. Gutenberg-Richter b-value of earthquake distribution and correlation fractal dimension (D2) are estimated for 493 earthquakes with magnitude of completeness 3.6 prior to this earthquake. We consider earthquakes in western Nepal Himalaya and adjoining region (80.0–83.5°E and 27.3–30.5°N) for the period of 1964 to 2022 for the analysis. The b-value 0.68±0.03 implies a high stress zone and the spatial correlation dimension 1.81±0.02 implies a highly heterogeneous region where the epicenters are spatially distributed. Low b-values and high D2 values identify the study region as a high hazard zone. Focal mechanism styles and low b-values correlate with thrust nature of earthquakes and show that the earthquake’s occurrence is associated with the dynamics of the faults responsible for generating the past earthquakes.


Unfunded studies
Enter: The author(s) received no specific funding for this work.

Introduction
The magnitude distribution of earthquakes, the spatial distribution of epicenter/hypocenter, frequency of aftershocks etc., satisfy the power law distribution (Pilgrim & Taylor, 2019;. Hence, earthquakes can be described by the scaling parameter obeying power law, known as the fractal dimension (Huang & Turcotte, 1988;Mandlebrot, 1989;Shcherbakov et al., 2005). The b-value of frequencymagnitude is a power law involving magnitude while the two-point spatial correlation dimension of earthquake's epicenter distribution displays a power law that quantifies the proportion of randomness and clusterization. The b-value measures the material heterogeneities within a fault zone and decreases with increasing stress in the brittle part of the earth's crust. It suggests an increase possibility of happening of large magnitude earthquakes (lower b-value) and smaller magnitude earthquakes (higher b-value) (Gulia & Wiemer, 2010;Ogata & Tsuruoka, 2016;Wyss et al., 2004). The mean value of b ranges from about 0.7 to about 1.0 for longer period (Arroyo-Solórzano & Linkimer, 2021; El-Isa, 2018; Ketthong & Pailoplee, 2012). The b-value linked with the dynamics of individual faults is universal whereas the fractal dimension of the fault network can vary depending on geological heterogeneity (Lomnitz-Adler, 1992). Different tectonic processes undergoing inside the earth generally activate the fault systems in asperity zones from where generous size earthquakes nucleate (Legrand, 2002;Roy et al., 2011) Nepal rests on the boundary of Eurasian plate and Indian plate with major faults parallel to its length, so always vulnerable to earthquakes Pei et al., 2016). From northern belt to the southern belt, the South Tibetan Detachment (STD), Main Central Thrust (MCT), Main Boundary Thrust (MBT), and Main Frontal Thrust (MFT) are major faults system in the Himalaya (Grandin et al., 2015;Upreti, 1999). The MCT, MBT, and MFT sole into a gentle dipping detachment called the Main Himalayan Thrust (MHT) (Sathiakumar & Barbot, 2021). The present-day convergence between the Indian and Eurasian plates is mostly accommodated along the MHT whose surface trace is MFT. Along with these major faults, some northeast-southwest trending transverse lineaments like Tanakpur lineament, Karnali lineament, and Samea lineament are also responsible for seismicity activity of the western Nepal (Paudyal et al., 2010). In the past work related with anomalous seismicity of western Nepal Himalaya, potential zone for the medium size earthquakes was identified within an area bounded by 29.3°-30.5°N and 81.2°-81.9°E (Paudyal & Singh, 2008). The recent work identified the existence of asperity capable of hosting the future earthquake with similar character of the 2015 Gorkha earthquake towards west of the epicenter of Gorkha earthquake (Sreejith et al., 2018). The research carried out by separate groups (Bilham, 2019;Mencin et al., 2016;Molnar & Pandey, 1989) highlights the presence of a crucial seismic gap in western Nepal and adjoining region. Thus, the prime objective of this paper is to characterize the stress level and heterogeneity of the seismogenic sources by mapping b-value and fractal dimension in the region.
In record, Nepal has the long history of moderate to large earthquakes since 1255 (Joshi & Kaushik, 2017). The western region of Nepal is seismically most active segment of central Himalaya and had also hosted many earthquakes in the past and few of them are notable (Paudyal et al., 2010). An earthquake of 26 September, 1964 (6.0 mb) occurred in Nepal-India border 4 km from Dharchula, Uttarakhand, India. The 6.0 mb earthquake on 27 June 1966, at the depth of 23.80 km in border of Nepal and India took the lives of 80 people (Agrawal, 1969). The 6.1 mb Bajhang earthquakes on July 29, 1980 affected Baitadhi, Bajhang and Darchula region of western Nepal and took 125 lives (Chaulagain et al., 2018;Khanal, 1997). Following the history, a magnitude 5.6 mb or 6.6 ML earthquake hit western Nepal in the wee hours of Wednesday morning local time (2:12 AM, 2022.11.08) killing at least six people (Pokharel & Wang, 2022). The epicenter of the quake was 21 km east of Dipayal (Headquarter of Doti District), at a depth of 15.7 km. Cracks have surfaced in most of the houses in the aftermath of the geological event. As per the National Earthquake Monitoring & Research Center (seismonepal.gov.np), a 5.7 ML earthquake was reported in the area at 9:07 pm prior to the stronger one that was felt later. Many aftershocks had been felt after the two bigger quakes throughout the night. The jolt was felt in and around Bajhang, Kailali, Kanchanpur, Banke, Rukum west and far up to the Indian capital Delhi and lasted for about 10 seconds (Joshi, 2022). The fault plane solutions from the catalog of Global Centroid Moment Tensor (GCMT) (Dziewonski et al., 1981;Ekström et al., 2012) depict the Doti earthquake as shallow angle north east dipping thrust fault event. The fault geometry of this earthquake is similar to the 1980, Bajhang earthquake ( Figure 1).  (2022) is represented by red star. Black sphere is indicating the Dipayal (Head quarter of Doti district). Tiny spheres (orange) indicate the earthquakes having magnitude between 3.6 and 5.0 and blue spheres indicate the earthquakes having magnitude between 5.1 and 6.0. Beach balls depict the focal mechanism solutions of July 29, 1980 Bajhang earthquake and 8 November, 2022 Doti earthquake. STD is South Tibetan Detachment, MCT is Main Central Thrust, MBT is the Main Boundary Thrust, and MFT is the Main Frontal Thrust. TL is the Tanakpur lineament, KL is Karnali lineament, and SL is Samea lineament (Paudyal et al., 2010).

Data and methodology
For better understanding of earthquake phenomena, a decent dataset is essential. The dataset used in this study is from the catalog of International Seismological Centre (ISC) (Bondár & Storchak, 2011;Storchak et al., 2020). We retrieved 634 earthquakes from the ISC catalog. After declustering and removing dependent events (Reasenberg, 1985), only 609 earthquakes were retained. The completeness magnitude (Mc) is checked by the ZMAP software (Wiemer, 2001) which gives only 493 events with Mc ≥ 3.6 for final analysis (Figure 2 and Figure 3). The final data set contains 442 events having magnitude between 3.6 and 4.9, 48 events having magnitude between 5.0 and 5.9, and three events having magnitude greater than equal to 6.0. To map the b-value and fractal dimension, the study area was gridded at 1°×1° spacing with an overlapping of 0.2°. The correlation dimension (D2) and b-value are estimated only for the grids containing events ≥ 25 for the reliable values of these parameters. The b-value is calculated by maximum likelihood estimation (MLE) method which has an advantage of not being influenced by large magnitude earthquakes. The formula for the estimation of b-value (Aki, 1965;Bender, 1983) with standard deviation (Shi & Bolt, 1982 Where Ma is average magnitude, M is minimum magnitude, and ∆M is binning width of the catalog. The spatial correlation dimension is calculated from correlation integral function ( ) (Mondal et al., 2019;Roy & Padhi, 2007) as, Where r is the scaling radius (r = 5 km to r = 35 km for this study), N is the number earthquakes in the sample grid, − is the angular distance between two events which can be evaluated by the spherical triangle method (Hirata, 1989)

Results and discussion
From the earthquake data of ISC catalog, we have estimated the b-value and fractal dimension of 39 grids following the procedure mentioned in data and methodology section and presented in table 1.  The b-value for whole data set is found to be 0.68 ± 0.03 while the b-value map shows the broad variation for different grids i.e., between 0.48 and 1.55 (Table 1 and Figure 3). This type of variation is acceptable for the seismically active Himalayan region (Gui et al., 2019;Zhu, 2021). The broad patch of low b-value between 0.48 and 0.64 is noticed for the region occupied by historical earthquakes and the recent Doti earthquake as well. These low b-values can also be linked with the reverse faulting mechanism of the region. The lower b-values are indicator of a more stressed zone or presence of asperity in the region (Kumar et al., 2013;Nakaya, 2006). Thus, the area enclosed between Tanakpur Lineament and Samea lineament could be the host region of the future large earthquake. The north east corner of the study region is reflected with high b-value contours (1.00 to 1.50), so can be inferred as less probable region for the future large earthquake. Fractal dimension is a measure of resistance of material against the fracture, so the fragile material had a smaller fractal dimension (D2). The fractal dimension would increase with an increase in the energy density available for fracture (Bardeji, 2018;Turcotte, 1986). D2 is a measure of spatial clustering and can take a value from 0 to 2. Its value close to 0 signifies that earthquakes are centralized in a small locality and the value close to 2 signifies that the earthquakes are spatially distributed (Kagan, 2007;Mandal & Rodkin, 2011). The fractal dimension value 1.81 ± 0.02 for whole data set (Table 1 and Figure 4) and the variation between 1.36 and 1.92 for different grids indicate that the epicenters are distributed in 2D seismogenic structures. High D2 contours (1.5 to 1.92) are identified for the area occupied by the past moderate earthquakes and recent Doti earthquake. These areas could be inferred as the asperity zones along the fault systems. The areas east of Dipayal are identified as the low D2 contours (1.36 -1.52) area. The higher values of fractal dimensions obtained from this study suggest the presence of spatially distributed heterogeneous faults in the region and the region are seismically active. The smaller b-value zones (0.48 -0.60) are corroborated with higher D2 (1.5 -1.9), implying negative correlation. The areas with low b-value and high D2 and are expected to accumulate prominent levels of tectonic stress, which could be the risk factor for generating large earthquakes in the future (Mandal et al., 2022;Sarkar et al., 2020;Tiwari & Paudyal, 2021). The area identified as high risk zone in this study is within the zone identified as anomalous seismicity zone in the past work (Paudyal & Singh, 2008).

Conclusion
After the analysis of earthquake dataset for the period of 58 years (1964 -2022), the b-value earthquake distribution and the fractal dimension (D2) of epicenter distribution are mapped for the tectonic structures of western Nepal and adjoining region. The maximum likelihood method is used for the estimation of bvalue and correlation integral method is employed for the estimation of fractal dimension. The results identify the region under study as a high hazard zone with low b-values and high D2 values. A high D2 value obtained for the region indicates strong heterogeneity at this part of the Himalaya may be due to varied stress level in the crust. The fault geometry of 2022 Doti earthquake and 1980 Bajhang earthquake revealed by focal mechanism solutions show the similar characteristics, so the occurrence of the earthquake could be related to the previous earthquakes. The mapped region can be inferred to be most hazardous, which correlate well with seismic gap mentioned in the past literature. Finally, this study sheds new light in the understanding the characteristics of the seismogenic sources in western Nepal Himalaya.